I'd like to make a general comment about estimating probabilities for these kinds of discussions, if I may.
When we are interested in finding out about, e.g. likelihood of what kind of ship is being built here, the statistical term for this is called finding the marginal distribution of a random variable. In this case the variable is "type of ship". For simplicity, lets say our variable is either "carrier" or "not a carrier". When we have observations to base our estimates on, what we are doing statistically is called "conditioning". The formal way to put this is that we are comparing the probabilities of "type of ship is carrier" conditioned on "observations" and "type of ship is not carrier" conditioned on "observations".
One needs to be careful to not confuse conditioning "type of carrier" given "observation" with conditioning "observation" with "type of carrier". For example, saying that "carriers are unlikely to be built bow forward" is to say that the probability of "building bow forward" conditioned on "type of ship is carrier" is low. This is a different (and potentially unrelated) statement from saying "if it is built bow forward, it is unlikely to be a carrier" which is to estimate the probability of "type of ship is carrier" given "built bow forward". (For interested readers, the way these two statements are generally related is through Bayes' rule)
A principle to keep in mind is that, conditioning on observations will only change the marginal distribution (likelihood of different types of ships) if that observation makes one possibility more likely than another. In particular, the likelihood of seeing that observation does not matter. Even if an observation is extremely rare, for example (hypothetically) a ship being built in a weird way like having multiple sections scrambled up, this doesn't always say anything about whether "carrier" or "not a carrier" is more likely.
What we need to keep in mind when we are trying to determine the value of statements such as "carriers are unlikely to be built bow forward" is whether "not-carriers are more likely to be built bow forward"(*). If both are equally unlikely, then the statistical term for that is that "direction of bow" is independent from "type of ship", which means that "direction of bow" doesn't tells us anything about whether this is likely to be a carrier or not. Likewise, if both are about equally likely, that doesn't help us either. It is the difference, and only the difference, that matters.
(*) note: this is simplifying things slightly, and assumes that the "prior" is unbiased. In this case, you need to multiply (respectively) by the probability of a carrier or not-carrier being built, in general and agnostic of any observations. This can be estimated by build rates for either.
When we are interested in finding out about, e.g. likelihood of what kind of ship is being built here, the statistical term for this is called finding the marginal distribution of a random variable. In this case the variable is "type of ship". For simplicity, lets say our variable is either "carrier" or "not a carrier". When we have observations to base our estimates on, what we are doing statistically is called "conditioning". The formal way to put this is that we are comparing the probabilities of "type of ship is carrier" conditioned on "observations" and "type of ship is not carrier" conditioned on "observations".
One needs to be careful to not confuse conditioning "type of carrier" given "observation" with conditioning "observation" with "type of carrier". For example, saying that "carriers are unlikely to be built bow forward" is to say that the probability of "building bow forward" conditioned on "type of ship is carrier" is low. This is a different (and potentially unrelated) statement from saying "if it is built bow forward, it is unlikely to be a carrier" which is to estimate the probability of "type of ship is carrier" given "built bow forward". (For interested readers, the way these two statements are generally related is through Bayes' rule)
A principle to keep in mind is that, conditioning on observations will only change the marginal distribution (likelihood of different types of ships) if that observation makes one possibility more likely than another. In particular, the likelihood of seeing that observation does not matter. Even if an observation is extremely rare, for example (hypothetically) a ship being built in a weird way like having multiple sections scrambled up, this doesn't always say anything about whether "carrier" or "not a carrier" is more likely.
What we need to keep in mind when we are trying to determine the value of statements such as "carriers are unlikely to be built bow forward" is whether "not-carriers are more likely to be built bow forward"(*). If both are equally unlikely, then the statistical term for that is that "direction of bow" is independent from "type of ship", which means that "direction of bow" doesn't tells us anything about whether this is likely to be a carrier or not. Likewise, if both are about equally likely, that doesn't help us either. It is the difference, and only the difference, that matters.
(*) note: this is simplifying things slightly, and assumes that the "prior" is unbiased. In this case, you need to multiply (respectively) by the probability of a carrier or not-carrier being built, in general and agnostic of any observations. This can be estimated by build rates for either.
Last edited:
